When operating gas or steam turbines, a safe distance from bending-critical speeds must be ensured in terms of operating speed. This assumes that these can be reliably determined during the design phase. If there are no FEM models yet, the turbine developer likes to use simple beam models that can be easily solved numerically. Since, neglecting gyroscopic effects, the critical bending speed is equal to the first natural bending frequency of the rotor, the accuracy of the simple calculation depends on the exactness of the assumed equivalent bending stiffness of the turbine disks placed over a Hirth toothing. Due to the geometry of the turbine disks, additional inverting effects occur during bending deformation, which influence the bending stiffness. For this purpose, FEM models of the turbine disks were statically loaded and the equivalent bending stiffnesses were determined from the deformation. By automatically varying the disk geometry, replacement stiffnesses could be determined largely automatically for a large number of turbine disks. By solving overdetermined systems of equations, approximate formulas could be derived that enable the bending stiffness of a turbine disk to be calculated by specifying important geometric dimensions.
